Weak Solutions, A Priori Estimates

2009 ◽  
pp. 19-41
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Priori Estimates

Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740002
Author(s):  
Sławomir Kołodziej
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Stability Of Solutions ◽  
Hermitian Manifolds ◽  
Priori Estimates ◽  
Existence And Stability ◽  
Monge Ampere

In this paper, we describe how pluripotential methods can be applied to study weak solutions of the complex Monge–Ampère equation on compact Hermitian manifolds. We indicate the differences between Kähler and non-Kähler setting. The results include a priori estimates, existence and stability of solutions.

Some fundamental a priori estimates for weak solutions of the evolution p-Laplacian equation

2019 ◽  
Vol 99 (16) ◽  
pp. 2793-2806
Author(s):  
J. S. Ziebell ◽  
L. Schütz ◽  
P. L. Guidolin
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Laplacian Equation ◽  
Priori Estimates

scholarly journals On travelling wave solutions of a model of a liquid film flowing down a fibre

2021 ◽  
pp. 1-30
Author(s):  
HANGJIE JI ◽  
ROMAN TARANETS ◽  
MARINA CHUGUNOVA
Keyword(s):  
Thin Film ◽  
Weak Solutions ◽  
A Priori Estimates ◽  
Travelling Waves ◽  
A Priori ◽  
Travelling Wave ◽  
Model Parameters ◽  
Priori Estimates ◽  
Thin Film Model ◽  
Long Time

Abstract Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals. Long-time behaviour of these weak solutions is analysed and, under some additional constraints for the model parameters and initial values, convergence towards a travelling wave solution is obtained. Numerical studies of energy minimisers and travelling waves are presented to illustrate analytical results.

scholarly journals CONVERGENCE OF THE SOLUTIONS ON THE GENERALIZED KORTEWEG–DE VRIES EQUATION∗

2016 ◽  
Vol 21 (2) ◽  
pp. 239-259 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Compensated Compactness ◽  
Dispersive Equation ◽  
Priori Estimates ◽  
Scalar Conservation Law ◽  
De Vries ◽  
Scalar Conservation

We consider the generalized Korteweg-de Vries equation, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the Lp setting.

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